It was their third double of the season and it left coach Paul Trollope predicting his side can still be in there with a shout if they win their last five games.
The odds are long but a positive approach showed their self-belief is high as they got the better of Bury.
Before they hit their stride, though, Rovers were twice close to being hurt. The game was only two minutes old when John Fitzgerald thundered a shot against the middle of the bar and then his co-central defender Dave Challinor drew a hurried dive from Steve Phillips with the follow-up shot.
The burst of action followed a needless corner given away by Craig Hinton and then some uncertain defending gave Bury another chance when William Mocquet volleyed a long Challinor throw-in a fraction too high.
Rovers gradually got on top, pushed their by the pace of Lewis Haldane down the right, and with a good supporting service coming from full-back Aaron Lescott.
They passed up chances when Hinton failed to make proper contact with a free header followed by an angled shot from Richard Walker which grazed the far post on its way out.
Walker quickly redeemed himself with a sharp inside pass which put Lambert in for his opening goal as the half hour came up. The big striker, a £200,000 signing from Rochdale in the autumn, had time to turn and steady himself before delivering a low shot comfortably inside the far post.
Bury were deflated by the goal and were clearly rattled as Challinor rebuked his keeper Andy Warrington.
They rallied briefly when Andy Bishop saw his effort fly just wide of the near post at the start of the second half, but were dealt a hammer blow on the hour.
Colin Woodthorpe brought Haldane down to the right of goal earning a long lecture from referee Andy D'Urso. Haldane's resulting kick bobbled awkwardly on its 10-yard journey, but Lambert hooked his right leg well over it to send a not very convincing volley past the keeper's left hand.